In the given scenario, we have parallel lines \(PQ \parallel RS\) and we need to find the measure of angle \(m\angle RWU\) while knowing that \(m\angle PVT = 109^\circ\).
When parallel lines are cut by a transversal, several angle relationships occur:
- Alternate interior angles are equal.
- Corresponding angles are equal.
- Consecutive interior angles are supplementary (they add up to 180°).
Given that \(m\angle PVT = 109^\circ\), you can identify the relationship between \(m\angle PVT\) and \(m\angle RWU\).
Assuming \(V\) and \(W\) are points on the transversal, and \(T\) is where the transversal intersects line \(PQ\), we can identify the angle \(RWU\) based on the properties of parallel lines.
Since \(PVT\) and \(RWU\) are alternate interior angles (assuming they are situated as such), we have that:
\[ m\angle RWU = m\angle PVT = 109^\circ \]
So if \(RWU\) is not an alternate interior angle, we have to know the exact position, but it does not seem it is supplementary to \(PVT\) in this configuration.
However, if \(RWU\) is an outside angle related to another angle, for example, if we want to find a different angle alongside with it, we need to supplement. Therefore if \(RWU\) is related more directly,
If \(m\angle RWU\) is supplementary to \(m\angle PVT\), it would be:
\[ m\angle RWU + 109^\circ = 180^\circ \]
So:
\[ m\angle RWU = 180^\circ - 109^\circ = 71^\circ \]
Based on this reasoning, the answer would be:
71°
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